MCQ Class 10, Some Applications Of Trigonometry Set II

1. There will be total 20  MCQ in this test.
2. Please keep a pen and paper ready for rough work but keep your books away.
3. The test will consist of only objective type multiple choice questions requiring students to mouse-click their correct choice of the options against the related question number.
4. No negative marking for incorrect choice.
5. Please click on “Finish the Test” when you want to exit.
6. All the best – Happy Studying

1. The shadow of a tower standing on a level ground is found to be 40 m longer when the Sun's altitude is 30° than when it is 60°. Find the height of the tower.

20

40√3

20√3

40

Question 1 of 20

2. The angle of depression of a car, standing on the ground, from the top of a 75 m high tower, is 30°. The distance of the car from the base of the tower (in m.) is:

75√3

25√3

150

50√3

Question 2 of 20

3. A 20 m long ladder touches the wall at a height of 10 m. The angle which the ladder makes with the horizontal is

30°

45°

60°

90°

Question 3 of 20

4. Consider a ladder which makes an angle of 60° with a wall of height 10 m and its top just touches the top of the wall. If the ladder is now rotated in such a way that its top now touches the top of the opposite wall which has a height of 10/√3 m. What is the angle by which the ladder is rotated.

45°

60°

90°

30°

Question 4 of 20

5. A tree is broken by wind and its upper part touches the ground at a point 10 metres from the foot of the tree and makes an angle of 45° with the ground. The entire length of the tree is

20 m

10 (1 + √2) m

10√2 m

10 m

Question 5 of 20

6. A man has to clean a window at a height of 5 m on a building. He needs to reach a point 1.3m below the window to clean it. What should be the length of the ladder that he should use which, when inclined at an angle of 60° to the horizontal, would enable him to reach the required position?

2.46

2√3

2.46/ √3

2.46√3

Question 6 of 20

7. The angle of elevation from a point 30 feet from the base of a pole, of height h, as level ground to the top of the pole is 45° degree. Which equation can be used to find the height of the pole.

tan 45° = 30/h

tan 45° = h/30

sin 45° = h/30

cos 45° = h/30

Question 7 of 20

8. A man on a top of a tower observes a truck at an angle of depression α where tanα = 1/ √5 and sees that it is moving towards the base of the tower. Ten minutes later, the angle of depression of the truck is found to be β where tan β = √5 . If the truck is moving at a uniform speed, then how much more time it will take to reach the base of the tower.

150√5 sec

1500 sec

150 sec

150/ √5 sec

Question 8 of 20

9. The -------- is the line drawn from the eye of an observer to the point in the object viewed by the observer

Line of sight

Line of sight propagation

Line of symmetry

Line of incidence

Question 9 of 20

10. A kite is flying at a height of 75 metres from the ground level, attached to a string inclined at 60° to the horizontal. The length of the string to the nearest metre is

55 m

87 m

100 m

60 m

Question 10 of 20

11. Consider a ship with a right triangular mast. If the base of the mast is 10 m long, and the angle that the mast makes with the base is 60°, then what area of cloth is used to make the mast?

50 (√3 + 1) m²

50 √3 m²

50 m²

100 m²

Question 11 of 20

12. A ladder leaning against a wall makes an angle of 60° with the wall. If its foot is 6.2 m away from the wall, its length is

10.2 m

8 m

14.2 m

12.4 m

Question 12 of 20

13. The angle of depression from the top of a tower 12 m high, at a point on the ground is 30°. The distance of the point from the top of the tower is:

12√3 m

24 m

6 m

12 m

Question 13 of 20

14. If the angles of depression from the top of a tower of height 40 m to the top and bottom of a tree are 45° and 60° respectively, then the height of the tree is

A

B

C

D

Question 14 of 20

15. Consider a ship with a right triangular mast. If the base of the mast is 10 m long, and the angle that the mast makes with the base is 60°, then what area of cloth is used to make the mast?

50 (√3 + 1) m²

50 √3 m²

50 m²

100 m²

Question 15 of 20

16. In the given figure, the respective values of y and x are

60° and 30°

45° and 60°

60° and 45°

30° and 45°

Question 16 of 20

17. In the given figure, the respective values of y and x are

60° and 30°

45° and 60°

60° and 45°

30° and 45°

Question 17 of 20

18. The angle of elevation of the sun when the length of the shadow of the tree is √3 times the height of the tree is

90°

30°

60°

45°

Question 18 of 20

19. If the angle of the top of the 200 m high tower from a point C on the ground is 30°. The distance of the point C from the foot of the tower is
(Take √3 = 1.732)

346.4 m

173.6 m

300.4 m

246.6 m

Question 19 of 20

20. If sun's elevation is 60° then a pole of height 6 m will cast a shadow of length

3√2 m

2√3 m

6√3 m

√3 m

Question 20 of 20

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